Green Party Presidential Nominee Jill Stein's recent requests for recounts in Pennsylvania, Michigan and Wisconsin highlight how few states routinely verify the accuracy of their vote counts: Twenty-two states do not require a post-election audit, and 15 states do not require paper records that could be compared against electronic vote tallies in a recount.

With roughly 22.5 percent of registered voters living in election districts with paperless ballots, the pressure to audit vote counts is mounting. Modern electronic machines are susceptible to tampering, casting doubt on the security of the machines and the certainty of their final vote counts.

Following the 2000 presidential election and the resulting legal challenges in Florida over inaccurate counts of votes cast on paper ballots, Congress distributed more than $3 billion to replace manual voting equipment with modern electronic machines. At the time, "there was a feeling among some election officials and state legislatures that it'd be best to avoid paper going forward," said Larry Norden, deputy director of the Democracy Program at the Brennan Center for Justice. Instead, states opted for "computerized voting machines that just told you what the totals were and you wouldn't have to deal with the messy process of trying to figure out voter intent."

But as it's become clear that without a paper record there's no way to verify vote tallies, computer scientists and election activists have begun pushing for states to not only keep a paper record but to also institute routine post-election audits. Since 2004, many states passed a law requiring audits.

In some cases, it's taken a crisis to convince state officials that an auditable paper trail is necessary.

In 2004, a statewide race for North Carolina agriculture commissioner came down to about 2,300 votes. More than 4,000 votes were lost during the early voting period when a single voting machine received more votes than its storage would allow. Without a paper trail, there was no way to know if the lost votes would have changed the outcome of the election. To avoid the situation going forward, the legislature mandated paper records and routine post-election audits in each county.

Lack of funding is the main reason some states don't have paper audits, said Pam Smith with Verified Voting, an organization that advocates for legislation and regulation that promotes the verifiability of elections. Shortly after the 2000 presidential election, many states were able to make use of federal grants to update their equipment with a verifiable paper record. But once that money dried up, some state and local jurisdictions couldn't add paper ballots -- and that also meant no meaningful audits.

New Jersey, for example, passed a law in 2008 that was similar to the one in North Carolina, but the estimated cost of retrofitting existing machines with paper ballots would have been an extra $2,000 per voting machine. In the middle of the Great Recession, lawmakers decided to wait until the economy improved. To date, New Jersey still does not have a paper trail and routine audits.

As recently as 2014, three states added or strengthened post-election audit requirements, according to the National Conference of State Legislatures. Massachusetts established audits, Virginia made permanent a pilot version of its audit program and Vermont made audits mandatory, rather than at the discretion of the Secretary of State.

States do take a number of precautions besides post-election paper audits to make sure votes get tallied correctly. They test equipment before and after elections to ensure they are operating properly. They may also run “procedural” audits after an election to check that poll workers followed standard processes and that all cast ballots were counted.

But these precautions do not address the potential problem of a hacker altering people’s votes from the point they fill out their ballot to the point that machine counts it.

In late November, J. Alex Halderman, a computer scientist from the University of Michigan, called attention to the importance of paper records at a time when many were concerned about the prospect of hackers swinging the outcome of the election.

"Paper creates a record of the vote that can't be later modified by any bugs, misconfiguration, or malicious software that might have infected the machines," he explained in a blog post.

After Nov. 8, Halderman contacted Hillary Clinton's campaign and argued in favor of recounts in Michigan, Pennsylvania, and Wisconsin to verify for certain that the results weren't manipulated.

While Halderman and the Stein campaign have called attention to the issue, post-election audits are different from full recounts. Audits sample a small fraction of the overall vote count to see if electronic tallies made any kind of systematic error -- misreading smudges as votes, for instance.

Where the audits and recounts overlap is in their shared need for a paper record to compare against electronic vote tallies. In Pennsylvania, about 6.7 million registered voters lived in districts with paperless ballots. If their votes were counted incorrectly by a machine because of a virus or a programming error, election officials may only have a digital record of the incorrect vote. In that case, they wouldn't be able to determine voters' intent.

Of the three states undergoing a recount in December, only Pennsylvania lacks a verifiable paper record in most parts of the state.

Given concerns about the security of voting systems, states without mandatory post-election audits are likely to consider legislation next year.

"I do expect to see changes," said Smith, "and I think the direction they would go is toward paper."

Paper audit trails would add a recurring cost for election officials, but they might improve voters' confidence in the accuracy of the final results. And, as the Brennan Center's Norden noted, "audits are a lot of cheaper than recounts."